Order of Operations: Polynomials and Exponents

Date: 9/10/96 at 10:26:25
From: Heidy Man
Subject: Polynomials and Exponents

I'm stuck on 3*5-4^2, (3*5-4)^2, -6^2*2, (-6*2)^2 .

Date: 9/10/96 at 16:40:13
From: Doctor Ana
Subject: Re: Polynomials and Exponents

These questions are really about order of operations. You need to know 
what to do first in order to be able to solve them.

You should remember from arithmetic that multiplication and division 
come before addition and subtraction. (A good way to remember that is 
My Dear Aunt Sally). When we get into exponents, we have to expand the 
list to tell us what to do first.

The first thing we will do is to evaluate anything that is inside of 
parentheses.

(1) 3 x 5 - 4^2

(2) (3 x 5 - 4)^2 = (15-4)^2 = (11)^2

(3) -6^2 x 2

(4) (-6 x 2)^2 = (-12)^2

The next thing we will do is to evaluate all of the exponents.  You 
have to be careful here: in (1) the 4 is the only thing that is 
squared, in (2) the 11 inside the parentheses is squared, in (3) the 
6 is squared and then multiplied by -1 to get the negative sign, and 
in (4) negative 12 is squared. It is very important to know whether a 
negative number is going to be squared or not. Unless it is inside of 
parentheses, it will NOT be squared, and you have to remember to keep 
it with the number that is negative.

After you evaluate all of the numbers that are squared, then you can 
finish up the multiplication, addition and subtraction to get your 
answer. The big thing is to do everything inside of the parentheses 
first.

Do all multiplication and division, and all addition and subtraction 
left-to-right.

-Doctor Ana,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/